Randall Stephenson, CEO of AT&T, says his company does not need to buy assets from América Móvil SAB to be successful in Mexico.

The opportunity for AT&T to expand into Mexico is huge, especially considering Internet on mobile phones has not really taken off yet in that country.

"We believe we have found a path that gets us a nice, scalable growth platform without the América Móvil assets," said Stephenson in an interview. "If things materialize over time and those assets look attractive we would obviously have to look at them, but we really don't need the América Móvil assets to be successful."

América Móvil, run by CEO Carlos Slim, is the largest mobile carrier in Mexico, with more than 70 percent market share. Not only that, but it has been looking to sell some of its wireless and landline assets to comply with regulations in Mexico aimed at promoting competition.

A number of other companies have also said they are uninterested in América Móvil's offerings, including Verizon, which has no interest in acquisitions in Mexico, and Vodafone, which has said it is unlikely to be interested.

The news comes shortly after it was announced that AT&T has entered an agreement to buy Mexican carrier Iusacell for $2.5 billion. The deal is likely to close by the end of the first quarter in 2015. The carrier Iusacell currently has a market share of 8 percent in Mexico, and is the third-largest mobile carrier in the country.

While AT&T is not interested in buying assets from América Móvil, Stephenson went on to say the company might be interested in buying the Mexican assets of Nextel, which has 2.8 million subscribers in the country. Currently, 28 percent of people in Mexico use a smartphone, a number that is likely to increase rapidly in the short-term as the price of mobile Internet service goes down and competition increases.

AT&T has had a relationship with América Móvil for 24 years, first starting when Southwestern Bell, AT&T's predecessor, helped Carlos Slim privatize and acquire América Móvil, which was state-run at the time. Historically, AT&T has had a 9 percent stake in América Móvil. This changed, however, when AT&T proposed to buy DirecTV for $48.5 billion in May of this year. DirecTV is a competitor of América Móvil, creating a conflict of interest for AT&T. Thus, the company sold its 8.3 percent stake in América Móvil back to the company in June.